Abstract

We discuss theoretically and demonstrate experimentally the robustness of the adiabatic sum frequency conversion method. This technique, borrowed from an analogous scheme of robust population transfer in atomic physics and nuclear magnetic resonance, enables the achievement of nearly full frequency conversion in a sum frequency generation process for a bandwidth up to two orders of magnitude wider than in conventional conversion schemes. We show that this scheme is robust to variations in the parameters of both the nonlinear crystal and of the incoming light. These include the crystal temperature, the frequency of the incoming field, the pump intensity, the crystal length and the angle of incidence. Also, we show that this extremely broad bandwidth can be tuned to higher or lower central wavelengths by changing either the pump frequency or the crystal temperature. The detailed study of the properties of this converter is done using the Landau-Zener theory dealing with the adiabatic transitions in two level systems.

© 2009 Optical Society of America

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References

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  1. F. Bloch, "Nuclear Induction", Phys. Rev. 70, 460-474 (1946).
    [CrossRef]
  2. R. P. Feynman, F. L. Vernon, and R.W. Hellwarth, "Geometrical Representation of the Schrodinger Equation for Solving Maser Problems", J. Appl. Phys. 28, 49-52 (1957).
    [CrossRef]
  3. H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, "Geometrical Representation of Sum Frequency Generation and Adiabatic Frequency Conversion", Phys. Rev. A,  78, 063821 (2008).
    [CrossRef]
  4. D. Boyd, Nonlinear Optics, 2nd ed. (Academic, New York, 2003).
  5. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1989).
  6. L. Allen and J. H. Eberly, Optical Resonance and Two Level Atoms (Dover, New York, 1987).
  7. T. Torosov and N. V. Vitanov, "Exactly soluble two-state quantum models with linear couplings", J. Phys. A,  41, 155309 (2008).
    [CrossRef]
  8. G. Imeshev, M. Fejer, A. Galvanauskas, and D. Harter, "Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings", J. Opt. Soc. Am. B 18, 534-539 (2001).
    [CrossRef]
  9. M. Arbore, A. Galvanauskas, D. Harter, M. Chou, and M. Fejer, "Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate" Opt. Lett. 22, 1341-1343 (1997).
    [CrossRef]
  10. G. Imeshev, M. Arbore, M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, "Ultrashort-pulse secondharmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping", J. Opt. Soc. Am. B,  17, 304-318 (2000).
    [CrossRef]
  11. D. S. Hum, and M. Fejer, "Quasi-phasematching", C. R. Physique 8, 180-198 (2007).
    [CrossRef]
  12. M. Charbonneau-Lefort, B. Afeyan, and M. Fejer, "Optical parametric amplifiers using chirped quasiphasematching gratings. I. Practical design formulas", J. Opt. Soc. Am. B 25, 463-480 (2008).
    [CrossRef]
  13. M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi phase matching in bulk polycrystalline isotropic nonlinear materials", Nature 432, 374-376 (2004).
    [CrossRef] [PubMed]
  14. K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, "Broadening of the Phase-Matching Bandwidth in Quasi-Phased-Matched Second Harmonic Generation", IEEE J. Quantum Electron 30, 15961604 (1994).
    [CrossRef]
  15. L. D. Landau, "Zur Theorie der Energieubertragung. II", Physics of the Soviet Union 2, 46-51 (1932).
  16. C. Zener, "Non-adiabatic Crossing of Energy Levels", Proc. Roy. Soc. London A 137, 696-702 (1932).
    [CrossRef]
  17. A. Massiach, Quantum Mechanics (N. Holland, Amsterdam, 1962), Vol II.
  18. D. J. Tannor, Introduction to Quantum Mechanics: A Time-dependent Perspective (University Science Books, Sausalito, California, 2007).
  19. J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric", Phys. Rev. 127, 1918-1939 (1962).
    [CrossRef]
  20. G. Rosenman, A. Skliar and D. Eger, M. Oron, and M. Katz, "Low temperature periodic electrical poling of flux-grown KTiOPO4 and isomorphic crystals", Appl. Phys. Lett.,  73, 3650-3652 (1998).
    [CrossRef]
  21. S. Emanueli, and A. Arie, "Temperature-Dependent Dispersion Equations for KTiOPO4 and KTiOAsO4", Appl. Opt. 42, 6661-6665 (2003).
    [CrossRef] [PubMed]

2008

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, "Geometrical Representation of Sum Frequency Generation and Adiabatic Frequency Conversion", Phys. Rev. A,  78, 063821 (2008).
[CrossRef]

T. Torosov and N. V. Vitanov, "Exactly soluble two-state quantum models with linear couplings", J. Phys. A,  41, 155309 (2008).
[CrossRef]

M. Charbonneau-Lefort, B. Afeyan, and M. Fejer, "Optical parametric amplifiers using chirped quasiphasematching gratings. I. Practical design formulas", J. Opt. Soc. Am. B 25, 463-480 (2008).
[CrossRef]

2007

D. S. Hum, and M. Fejer, "Quasi-phasematching", C. R. Physique 8, 180-198 (2007).
[CrossRef]

2004

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi phase matching in bulk polycrystalline isotropic nonlinear materials", Nature 432, 374-376 (2004).
[CrossRef] [PubMed]

2003

2001

2000

1998

G. Rosenman, A. Skliar and D. Eger, M. Oron, and M. Katz, "Low temperature periodic electrical poling of flux-grown KTiOPO4 and isomorphic crystals", Appl. Phys. Lett.,  73, 3650-3652 (1998).
[CrossRef]

1997

1994

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, "Broadening of the Phase-Matching Bandwidth in Quasi-Phased-Matched Second Harmonic Generation", IEEE J. Quantum Electron 30, 15961604 (1994).
[CrossRef]

1962

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric", Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

1957

R. P. Feynman, F. L. Vernon, and R.W. Hellwarth, "Geometrical Representation of the Schrodinger Equation for Solving Maser Problems", J. Appl. Phys. 28, 49-52 (1957).
[CrossRef]

1946

F. Bloch, "Nuclear Induction", Phys. Rev. 70, 460-474 (1946).
[CrossRef]

1932

L. D. Landau, "Zur Theorie der Energieubertragung. II", Physics of the Soviet Union 2, 46-51 (1932).

C. Zener, "Non-adiabatic Crossing of Energy Levels", Proc. Roy. Soc. London A 137, 696-702 (1932).
[CrossRef]

Afeyan, B.

Arbore, M.

Arie, A.

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, "Geometrical Representation of Sum Frequency Generation and Adiabatic Frequency Conversion", Phys. Rev. A,  78, 063821 (2008).
[CrossRef]

S. Emanueli, and A. Arie, "Temperature-Dependent Dispersion Equations for KTiOPO4 and KTiOAsO4", Appl. Opt. 42, 6661-6665 (2003).
[CrossRef] [PubMed]

Armstrong, J.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric", Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Baudrier-Raybaut, M.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi phase matching in bulk polycrystalline isotropic nonlinear materials", Nature 432, 374-376 (2004).
[CrossRef] [PubMed]

Bloch, F.

F. Bloch, "Nuclear Induction", Phys. Rev. 70, 460-474 (1946).
[CrossRef]

Bloembergen, N.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric", Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Charbonneau-Lefort, M.

Chou, M.

Ducuing, J.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric", Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Eger, D.

G. Rosenman, A. Skliar and D. Eger, M. Oron, and M. Katz, "Low temperature periodic electrical poling of flux-grown KTiOPO4 and isomorphic crystals", Appl. Phys. Lett.,  73, 3650-3652 (1998).
[CrossRef]

Emanueli, S.

Fejer, M.

Fermann, M.

Feynman, R. P.

R. P. Feynman, F. L. Vernon, and R.W. Hellwarth, "Geometrical Representation of the Schrodinger Equation for Solving Maser Problems", J. Appl. Phys. 28, 49-52 (1957).
[CrossRef]

Galvanauskas, A.

Haidar, R.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi phase matching in bulk polycrystalline isotropic nonlinear materials", Nature 432, 374-376 (2004).
[CrossRef] [PubMed]

Harter, D.

Hellwarth, R.W.

R. P. Feynman, F. L. Vernon, and R.W. Hellwarth, "Geometrical Representation of the Schrodinger Equation for Solving Maser Problems", J. Appl. Phys. 28, 49-52 (1957).
[CrossRef]

Hum, D. S.

D. S. Hum, and M. Fejer, "Quasi-phasematching", C. R. Physique 8, 180-198 (2007).
[CrossRef]

Imeshev, G.

Kato, M.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, "Broadening of the Phase-Matching Bandwidth in Quasi-Phased-Matched Second Harmonic Generation", IEEE J. Quantum Electron 30, 15961604 (1994).
[CrossRef]

Katz, M.

G. Rosenman, A. Skliar and D. Eger, M. Oron, and M. Katz, "Low temperature periodic electrical poling of flux-grown KTiOPO4 and isomorphic crystals", Appl. Phys. Lett.,  73, 3650-3652 (1998).
[CrossRef]

Kupecek, Ph.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi phase matching in bulk polycrystalline isotropic nonlinear materials", Nature 432, 374-376 (2004).
[CrossRef] [PubMed]

Landau, L. D.

L. D. Landau, "Zur Theorie der Energieubertragung. II", Physics of the Soviet Union 2, 46-51 (1932).

Lemasson, Ph.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi phase matching in bulk polycrystalline isotropic nonlinear materials", Nature 432, 374-376 (2004).
[CrossRef] [PubMed]

Mizuuchi, K.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, "Broadening of the Phase-Matching Bandwidth in Quasi-Phased-Matched Second Harmonic Generation", IEEE J. Quantum Electron 30, 15961604 (1994).
[CrossRef]

Oron, D.

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, "Geometrical Representation of Sum Frequency Generation and Adiabatic Frequency Conversion", Phys. Rev. A,  78, 063821 (2008).
[CrossRef]

Oron, M.

G. Rosenman, A. Skliar and D. Eger, M. Oron, and M. Katz, "Low temperature periodic electrical poling of flux-grown KTiOPO4 and isomorphic crystals", Appl. Phys. Lett.,  73, 3650-3652 (1998).
[CrossRef]

Pershan, P.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric", Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Rosencher, E.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi phase matching in bulk polycrystalline isotropic nonlinear materials", Nature 432, 374-376 (2004).
[CrossRef] [PubMed]

Rosenman, G.

G. Rosenman, A. Skliar and D. Eger, M. Oron, and M. Katz, "Low temperature periodic electrical poling of flux-grown KTiOPO4 and isomorphic crystals", Appl. Phys. Lett.,  73, 3650-3652 (1998).
[CrossRef]

Sato, H.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, "Broadening of the Phase-Matching Bandwidth in Quasi-Phased-Matched Second Harmonic Generation", IEEE J. Quantum Electron 30, 15961604 (1994).
[CrossRef]

Silberberg, Y.

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, "Geometrical Representation of Sum Frequency Generation and Adiabatic Frequency Conversion", Phys. Rev. A,  78, 063821 (2008).
[CrossRef]

Skliar, A.

G. Rosenman, A. Skliar and D. Eger, M. Oron, and M. Katz, "Low temperature periodic electrical poling of flux-grown KTiOPO4 and isomorphic crystals", Appl. Phys. Lett.,  73, 3650-3652 (1998).
[CrossRef]

Suchowski, H.

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, "Geometrical Representation of Sum Frequency Generation and Adiabatic Frequency Conversion", Phys. Rev. A,  78, 063821 (2008).
[CrossRef]

Torosov, T.

T. Torosov and N. V. Vitanov, "Exactly soluble two-state quantum models with linear couplings", J. Phys. A,  41, 155309 (2008).
[CrossRef]

Vernon, F. L.

R. P. Feynman, F. L. Vernon, and R.W. Hellwarth, "Geometrical Representation of the Schrodinger Equation for Solving Maser Problems", J. Appl. Phys. 28, 49-52 (1957).
[CrossRef]

Vitanov, N. V.

T. Torosov and N. V. Vitanov, "Exactly soluble two-state quantum models with linear couplings", J. Phys. A,  41, 155309 (2008).
[CrossRef]

Yamamoto, K.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, "Broadening of the Phase-Matching Bandwidth in Quasi-Phased-Matched Second Harmonic Generation", IEEE J. Quantum Electron 30, 15961604 (1994).
[CrossRef]

Zener, C.

C. Zener, "Non-adiabatic Crossing of Energy Levels", Proc. Roy. Soc. London A 137, 696-702 (1932).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

G. Rosenman, A. Skliar and D. Eger, M. Oron, and M. Katz, "Low temperature periodic electrical poling of flux-grown KTiOPO4 and isomorphic crystals", Appl. Phys. Lett.,  73, 3650-3652 (1998).
[CrossRef]

C. R. Physique

D. S. Hum, and M. Fejer, "Quasi-phasematching", C. R. Physique 8, 180-198 (2007).
[CrossRef]

IEEE J. Quantum Electron

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, "Broadening of the Phase-Matching Bandwidth in Quasi-Phased-Matched Second Harmonic Generation", IEEE J. Quantum Electron 30, 15961604 (1994).
[CrossRef]

J. Appl. Phys.

R. P. Feynman, F. L. Vernon, and R.W. Hellwarth, "Geometrical Representation of the Schrodinger Equation for Solving Maser Problems", J. Appl. Phys. 28, 49-52 (1957).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. A

T. Torosov and N. V. Vitanov, "Exactly soluble two-state quantum models with linear couplings", J. Phys. A,  41, 155309 (2008).
[CrossRef]

Nature

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi phase matching in bulk polycrystalline isotropic nonlinear materials", Nature 432, 374-376 (2004).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev.

F. Bloch, "Nuclear Induction", Phys. Rev. 70, 460-474 (1946).
[CrossRef]

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric", Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Phys. Rev. A

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, "Geometrical Representation of Sum Frequency Generation and Adiabatic Frequency Conversion", Phys. Rev. A,  78, 063821 (2008).
[CrossRef]

Physics of the Soviet Union

L. D. Landau, "Zur Theorie der Energieubertragung. II", Physics of the Soviet Union 2, 46-51 (1932).

Proc. Roy. Soc. London A

C. Zener, "Non-adiabatic Crossing of Energy Levels", Proc. Roy. Soc. London A 137, 696-702 (1932).
[CrossRef]

Other

A. Massiach, Quantum Mechanics (N. Holland, Amsterdam, 1962), Vol II.

D. J. Tannor, Introduction to Quantum Mechanics: A Time-dependent Perspective (University Science Books, Sausalito, California, 2007).

D. Boyd, Nonlinear Optics, 2nd ed. (Academic, New York, 2003).

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1989).

L. Allen and J. H. Eberly, Optical Resonance and Two Level Atoms (Dover, New York, 1987).

Supplementary Material (3)

» Media 1: MOV (2687 KB)     
» Media 2: MOV (1717 KB)     
» Media 3: MOV (2369 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Bloch sphere trajectories of SFG of three different intensities (a) (Media 1) 440MW/cm 2 (b) (Media 2) 80MW/cm 2 (c) (Media 3) 4MW/cm 2. The south-pole represents the amplitude of the input frequency, and the north-pole represents the amplitude of the converted frequency. (d) The projection of the trajectories onto the W axis yields the conversion efficiency along the propagation. In these trajectories, phase matching condition is fulfilled at z=1cm. The predicted output conversion efficiency for each trajectory, based on Eq. 4, is also presented. (e) Continuous adiabatic variation of the phase mismatch parameter is required. This can be achieved by slowly changing the poling periodicity along the propagation direction.

Fig. 2.
Fig. 2.

(a) The adiabatic sum frequency conversion apparatus. The detection stage was designed to detect both the incoming ω 1 beam, with the InGaAs detector, and the converted ω 3 beam, with the cooled CCD detection. (b) The monotonic relation between the growth of the converted beam (measured by a cooled CCD spectrometer) with the decrease of the incoming beam (measured by an InGaAs detector), when increasing the pump intensity.

Fig. 3.
Fig. 3.

Conversion efficiency as a function of input wavelength and the crystal length. (a) Two dimensional numerical simulation of the conversion efficiency as a function of input wavelength (y axis), and propagation distance. As seen, the shorter wavelengths are being converted early along the crystal, and the longer wavelengths are being converted as the crystal length is increased. (b) Experimental results of the spectral response in two different crystal length, 17 mm and 20 mm.

Fig. 4.
Fig. 4.

Conversion efficiency as a function of crystal temperature, using the adiabatic aperiodically poled KTP design at a pump intensity of 60MW/cm 2. (a) Two dimensional numerical simulation of the conversion efficiency as a function of crystal temperature (y-axis) and input wavelength. (b) Conversion efficiency as a function of crystal temperature at constant input wavelength of ω 1=1550nm. A good correspondence between the experimental results and the simulation of the design (vertical cross section of the two dimensional simulation) is shown.

Fig. 5.
Fig. 5.

Tunability of the broad bandwidth response. (a) Experimental results of temperature tunability, at pump intensity of 60MW/cm 2 Conversion efficiency. This shows a good agreement with the numerical simulations, presented in figure 4. (b) Numerical simulations of pump wavelength tunability.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

dA˜1dz+1vg1dA˜1dt=iκA˜3eiΔkz
dA˜3dz+1vg3dA˜3dt=iκ*A˜1e+iΔkz
dΔkdz(Δk2+κ2)32κ.
ηLZ(z)=1e4κ2πdΔkdz.
ηLZ(z)=1exp(25·32·103π2(χ(2))2I2n1n2n3λ1λ3cdΔkdz).
Δkeff(z)=k1(z)+k2(z)k3(z)+ΔkΛ(z)=Δkproc(z)+ΔkΛ(z).

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